Automatic analysis of electron backscatter diffraction patterns

Employing Constrained Nonnegative Matrix Factorization for Microstructure Segmentation

Materials characterization using electron backscatter diffraction (EBSD) requires indexing the orientation of the measured region from Kikuchi patterns. The quality of Kikuchi patterns can degrade due to pattern overlaps arising from two or more orientations, in the presence of defects or grain boundaries. In this work, we employ constrained nonnegative matrix factorization to segment a microstructure with small grain misorientations, (<1∘), and predict the amount of pattern overlap. First, we implement the method on mixed simulated patterns-that replicates a pattern overlap scenario, and demonstrate the resolution limit of pattern mixing or factorization resolution using a weight metric. Subsequently, we segment a single-crystal dendritic microstructure and compare the results with high-resolution EBSD. By utilizing weight metrics across a low-angle grain boundary, we demonstrate how very small misorientations/low-angle grain boundaries can be resolved at a pixel level. Our approach constitutes a versatile and robust tool, complementing other fast indexing methods for microstructure characterization.

A method for crystallographic mapping of an alpha-beta titanium alloy with nanometre resolution using scanning precession electron diffraction and open-source software libraries

An approach for the crystallographic mapping of two-phase alloys on the nanoscale using a combination of scanned precession electron diffraction and open-source python libraries is introduced in this paper. This method is demonstrated using the example of a two-phase α/β titanium alloy. The data were recorded using a direct electron detector to collect the patterns, and recently developed algorithms to perform automated indexing and analyse the crystallography from the results. Very high-quality mapping is achieved at a 3 nm step size. The results show the expected Burgers orientation relationships between the α laths and β matrix, as well as the expected misorientations between α laths. A minor issue was found that one area was affected by 180° ambiguities in indexing occur due to this area being aligned too close to a zone axis of the α with twofold projection symmetry (not present in 3D) in the zero-order Laue Zone, and this should be avoided in data acquisition in the future. Nevertheless, this study demonstrates a good workflow for the analysis of nanocrystalline two- or multi-phase materials, which will be of widespread use in analysing two-phase titanium and other systems and how they evolve as a function of thermomechanical treatments.

Robust methodology for the EBSD local misorientation analysis of surface cold work

The amount of cold work induced by a surface hardening technique and the depth to which it is produced within a metallic material are both important parameters within the field of surface engineering. In this paper a methodology of establishing reliable estimates of the depth and magnitude of cold work in surface hardened nickel-based superalloy single crystals from a dataset (map) of electron backscattered diffraction images through the analysis of local misorientations is described in detail. The impact of varying a number of acquisition parameters within the scanning electron microscope and the impact of the various post-acquisition analysis parameters on the outcome of the analysis are both described and discussed in detail. The Python script used to perform this analysis is published in full. The principles and processes underlying this methodology, as well as the published script, can be readily adapted for the analysis of datasets of electron backscattered diffraction images from other surface hardening techniques and other surface-hardened materials.

Diffraction-Based Multiscale Residual Strain Measurements

Modern analytical tools, from microfocus X-ray diffraction (XRD) to electron microscopy-based microtexture measurements, offer exciting possibilities of diffraction-based multiscale residual strain measurements. The different techniques differ in scale and resolution, but may also yield significantly different strain values. This study, for example, clearly established that high-resolution electron backscattered diffraction (HR-EBSD) and high-resolution transmission Kikuchi diffraction (HR-TKD) [sensitive to changes in interplanar angle (Δθθ)], provide quantitatively higher residual strains than micro-Laue XRD and transmission electron microscope (TEM) based precession electron diffraction (PED) [sensitive to changes in interplanar spacing (Δdd)]. Even after correcting key known factors affecting the accuracy of HR-EBSD strain measurements, a scaling factor of ∼1.57 (between HR-EBSD and micro-Laue) emerged. We have then conducted "virtual" experiments by systematically deforming an ideal lattice by either changing an interplanar angle (α) or a lattice parameter (a). The patterns were kinematically and dynamically simulated, and corresponding strains were measured by HR-EBSD. These strains showed consistently higher values for lattice(s) distorted by α, than those altered by a. The differences in strain measurements were further emphasized by mapping identical location with HR-TKD and TEM-PED. These measurements exhibited different spatial resolution, but when scaled (with ∼1.57) provided similar lattice distortions numerically.

A Denoising Autoencoder for Improved Kikuchi Pattern Quality and Indexing in Electron Backscatter Diffraction

The rapid collection and indexing of electron diffraction patterns as produced via electron backscatter diffraction (EBSD) has enabled crystallographic orientation and structural determination, as well as additional property-determining strain and dislocation density information with increasing speed, resolution, and efficiency. Pattern indexing quality is reliant on the noise of the collected electron diffraction patterns, which is often convoluted by sample preparation and data collection parameters. EBSD acquisition is sensitive to many factors and thus can result in low confidence index (CI), poor image quality (IQ), and improper minimization of fit, which can result in noisy datasets and misrepresent the microstructure. In an attempt to enable both higher speed EBSD data collection and enable greater orientation fit accuracy with noisy datasets, an image denoising autoencoder was implemented to improve pattern quality. We show that EBSD data processed through the autoencoder results in a higher CI, IQ, and a more accurate degree of fit. In addition, using denoised datasets in HR-EBSD cross correlative strain analysis can result in reduced phantom strain from erroneous calculations due to the increased indexing accuracy and improved correspondence between collected and simulated patterns.

Grain Boundary Plane Measurement Using Transmission Electron Microscopy Automated Crystallographic Orientation Mapping for Atom Probe Tomography Specimens

Grain boundaries are critical in determining the properties of materials, including mechanical stability, conductivity, and corrosion resistance. The specific properties of materials depend not only on the misorientation of the crystals, the three most commonly characterized parameters, but also on the angle of the grain boundary plane between the two crystals, the final two parameters in the five-parameter macroscopic description of the grain boundary. The method presented here allows for the direct measurement of all five parameters of the grain boundary in a transmission electron microscopy specimen of various morphologies. This is especially applicable to atom probe specimens, where only a single-tilt axis is generally available, allowing the crystallographic description to be matched to the detailed chemical data available in the atom probe tomography. This method provides a platform for efficient grain boundary analysis in unique samples, saving operator time and allowing for ease of acquisition and interpretation in comparison with traditional electron diffraction methods.

Machine learning based de-noising of electron back scatter patterns of various crystallographic metallic materials fabricated using laser directed energy deposition

A novel machine learning (ML) method of refining noisy Electron Back Scatter Patterns (EBSP) is proposed. For this, conditional generative adversarial networks (c-GAN) have been employed. The problem of de-noising the EBSPs was formulated as an image translation task conditioned on the input images to get refined/denoised output of EBSPs which can be indexed using conventional Hough transform based indexing algorithms. The ML model was trained using 10,000 EBSPs acquired under different settings for additively manufactured FCC, BCC and HCP alloy samples ensuring enough diversity and complexity in training data set. Pairs of noisy and corresponding optimal EBSPs were acquired by suitable tweaking of the EBSP acquisition parameters such as beam defocus, pattern binning and EBSD camera exposure duration. The trained model has brought out significant improvement in EBSD indexing success rate on test data, accompanied by betterment of indexing accuracy, quantified through 'pattern fit'. Complete automation of the EBSP refinement was demonstrated where in entire EBSD scan data can be fed to the model to get the refined EBSPs from which high quality EBSD data can be obtained.

Conditions near a crack tip: Advanced experiments for dislocation analysis and local strain measurement

The local stress state and microstructure near the crack-tip singularity control the fracture process. In ductile materials multiple toughening mechanisms are at play that dynamically influence stress and microstructure at the crack tip. In metals, crack-tip shielding is typically associated with the emission of dislocations. Therefore, to understand crack propagation on the most fundamental level, in situ techniques are required that are capable to combine imaging and stress mapping at high resolution. Recent experimental advances in x-ray diffraction, scanning electron microscopy, and transmission electron microscopy enable quantifying deformation stress fields from the bulk level down to the individual dislocation. Furthermore, through modern detector technology the temporal resolution has sufficiently improved to enable stress mapping during in situ experiments.

Microstructure analysis of 8 μm electrolytic Cu foil in plane view using EBSD and TEM

With the lightening of the mobile devices, thinning of electrolytic copper foil, which is mainly used as an anode collection of lithium secondary batteries, is needed. As the copper foil becomes ultrathin, mechanical properties such as deterioration of elongation rate and tear phenomenon are occurring, which is closely related to microstructure. However, there is a problem that it is not easy to prepare and observe specimens in the analysis of the microstructure of ultrathin copper foil. In this study, electron backscatter diffraction (EBSD) specimens were fabricated using only mechanical polishing to analyze the microstructure of 8 μm thick electrolytic copper foil in plane view. In addition, EBSD maps and transmission electron microscopy (TEM) images were compared and analyzed to find the optimal cleanup technique for properly correcting errors in EBSD maps.

Orientation, pattern center refinement and deformation state extraction through global optimization algorithms

Global optimization algorithms have been adopted to the simultaneously refinement of orientation and pattern center for electron backscatter diffraction patterns as well as deformation state extraction. The hyperparameter space and mutation schemes of differential evolution (DE) algorithm has been thoroughly investigated and showed to be a more efficient algorithm than the particle swarm optimization (PSO) algorithm. The optimal hyperparameters for DE generally depend on conditions such as the number of variables to be optimized and the size of bounded search space but reasonably close initial values for crossover probability is 0.9, mutation factor is 0.5, population size is ten times the number of variables, and number of iterations is at least 100. Validation on a set of simulated undeformed single crystal nickel patterns reveals a mean accuracy of ≈0.03° and ≈0.01% detector width across a large field of view. In addition, validation using noisy simulated deformed patterns with known deformation state and pattern center shows that the mean accuracy of shear strain and rotation components is ≈0.001 and for the normal strain ≈0.002.

Polynomial fitting method of background correction for electron backscatter diffraction patterns

A raw electron backscatter diffraction (EBSD) signal can be empirically decomposed into a Kikuchi diffraction pattern and a smooth background. For pattern indexing, the latter is generally undesirable but can reveal topographical, compositional, or diffraction contrast. In this study, we proposed a new background correction method using polynomial fitting (PF) algorithm to obtain clear Kikuchi diffraction patterns for some applications in nonconductive materials due to coating problems, at low accelerated voltage and at rough sample surfaces and for the requirement of high pattern quality in HR-EBSD. To evaluate the quality metrics of the Kikuchi patterns, we initially used three indices, namely, pattern quality, Tenengrad variance, and spatial–spectral entropy-based quality to detect the clarity, contrast, and noise of Kikuchi patterns obtained at 5 and 15 kV. Then, we examined the performance of PF method by comparing it with pattern averaging and Fourier transform-based methods. Finally, this PF background correction is demonstrated to extract the background images from the blurred diffraction patterns of EBSD measurements at low kV accelerating voltage and with coating layer, and to provide clear Kikuchi patterns successfully.

Automatic detection of Kikuchi bands based on Radon transform and PPHT

The information of crystal structure and orientation can be provided by analysing the EBSD (electron backscatter diffraction) patterns which are obtained with the EBSD devices. The reliability and accuracy of the information relies on the location of bands and intersections of the EBSD patterns. In this study, a method is proposed to automatically obtain the locations and intersections of the EBSD patterns, that is, Kikuchi bands. The proposed method uses Radon transform and progressive probabilistic Hough transform to detect straight lines and line segments of the Kikuchi band edges, respectively. Then, Kikuchi bands can be presented by fitting the hyperbolas with the endpoints of line segments. The results can numerically describe the information of Kikuchi bands. Experimental results show that the method is robust and can detect more accurate Kikuchi bands and intersections.

Local Kikuchi band detection in electron backscatter diffraction patterns for enhanced pattern indexing

Partially missing bands in the preset region for Hough transform might strongly affect the accuracy of indexing Kikuchi patterns and reduce the quality of electron backscatter diffraction (EBSD) maps. This paper proposes a novel local band detection method for such kind of low-quality patterns. The approach involves rotating bands to vertical direction, detecting the local line segments through calculating the largest horizontal average grey gradient with a constant interval of 400 pixels in vertical direction, and applying Hough transform as well as weighted averaging to these line clusters to unify the edges of Kikuchi band. Therefore, even if only part of a Kikuchi band is visible, the entire band can also be accurately extracted. The average interplanar angle error obtained by the proposed method is approximately 29.0% less than those obtained by Hough transform-based technique. Moreover, the comparison of mean angular deviation (MAD) is also discussed. The average MAD of this method is about 38.5% lower than that of Hough transform-based technique. Consequently, the local Kikuchi band detection method is expected to be used for post-processing and re-indexing the EBSD low-quality patterns.

Method for acquiring accurate coordinates of the source point in electron backscatter diffraction

An electron backscatter diffraction device is an important accessory for a scanning electron microscope and can provide crystal structure orientation and phase content data through analysis of electron backscatter diffraction patterns. The acquisition of these data depends on pattern indexing, including interplanar angle calculation and crystal plane indexation. The coordinates of the source point are key points for interplanar angle calculation, and they vary with the movement of the incident beam. In this study, we first combined the grey gradient calculation with screen moving method to achieve accurate positioning of source point and obtained coordinates of source point with sub-pixel precision. The errors of three coordinates were 0.07%, 0.06% and 0.04%, respectively. By using this coordinate of source point to conduct interplanar angle calculation the maximum error was 0.53°, which was a good proof of the accuracy of source point positioning. Then we established the relationship between source point coordinates variation and incident beam movement. Coordinates can be given out based on the displacement of beam directly. And to illustrate the accuracy, interplanar angle calculation was performed and the maximum error was 0.81°. This means that the relationship between variation of source point coordinates and beam movement is highly accurate.

Spherulitic and rotational crystal growth of Quartz thin films

To obtain crystalline thin films of alpha-Quartz represents a challenge due to the tendency for the material towards spherulitic growth. Thus, understanding the mechanisms that give rise to spherulitic growth can help regulate the growth process. Here the spherulitic type of 2D crystal growth in thin amorphous Quartz films was analyzed by electron back-scatter diffraction (EBSD). EBSD was used to measure the size, orientation, and rotation of crystallographic grains in polycrystalline SiO₂ and GeO₂ thin films with high spatial resolution. Individual spherulitic Quartz crystal colonies contain primary and secondary single crystal fibers, which grow radially from the colony center towards its edge, and fill a near circular crystalline area completely. During their growth, individual fibers form so-called rotational crystals, when some lattice planes are continuously bent. The directions of the lattice rotation axes in the fibers were determined by an enhanced analysis of EBSD data. A possible mechanism, including the generation of the particular type of dislocation(s), is suggested.

Identifying rotational symmetry axes in Kikuchi patterns by reciprocal vectors

Symmetry analysis of the Kikuchi pattern is helpful to determine the crystal structure, and can significantly reduce the screening range of phase identification, thereby improving the accuracy and reliability of phase identification in electron backscatter diffraction (EBSD). Accurately identifying the symmetry axis from the Kikuchi pattern is the primary task of symmetry analysis. In this study, a new method was proposed to identify symmetry axes in Kikuchi patterns with the aid of reciprocal vectors. Taking the Kikuchi patterns of single-crystal silicon as a typical example, a method for drawing reciprocal vectors after strict projection correction is introduced. The complex task of identifying the symmetry axis is transformed into an intuitive judgment of the geometric relationship between reciprocal vectors, thus greatly simplifying the process. This method successfully elucidated information on six Kikuchi poles in three single-crystal silicon Kikuchi patterns, including 3-fold axes, 4-fold axes and asymmetric axes. The method can also distinguish between a 3-fold axis and an analogous 3-fold axis despite their only slight differences.

Distribution rules of systematic absences and generalized de Wolff figures of merit applied to electron backscatter diffraction ab initio indexing

A new method for electron backscatter diffraction ab initio indexing is reported that adopts several methods originally invented for powder indexing. Distribution rules of systematic absences and error-stable Bravais lattice determination are used to eliminate the negative influence of non-visible bands and erroneous information from visible bands. In addition, generalized versions of the de Wolff figures of merit are proposed as a new sorting criterion for the obtained unit-cell parameters, which can be used in both orientation determination and ab initio indexing from Kikuchi patterns. Computational results show that the new figures of merit work well, similar to the original de Wolff Mn . The ambiguity of the indexing solutions is also pointed out, which happens in particular for low-symmetry cells and may generate multiple distinct solutions even if very accurate positions of band centre lines and the projection centre are given. It is supposed that this is the reason why indexing was successful in an orthorhombic case but not in a triclinic cell.

Factors affecting Confidence Index in EBSD analysis

Automated EBSD analysis systems have been used for over two decades relying on the fact that the correctness of a particular orientation solution could be assessed through the calculation of a Confidence Index. However, such an index only reports whether a particular solution stands out among any other possible solutions, by receiving a larger number of votes than others, and does not necessarily imply that the corresponding orientation is correct. This issue is addressed in the present paper, where the correctness of solutions and the factors that might affect it have been studied for single crystal Si and polycrystalline Zn. The results were compared to those presented in previous papers where this matter was studied in particular for an FCC material. It was observed that about 90% of the solutions were correct if they were obtained using a confidence index of 0.1 using at least 8 Hough bands regardless of the crystallographic structure or orientation.

Indexing of diffraction patterns for determination of crystal orientations

The task of determining the orientations of crystals is usually performed by indexing reflections detected on diffraction patterns. The well known underlying principle of indexing methods is universal: they are based on matching experimental scattering vectors to some vectors of the reciprocal lattice. Despite this, the standard attitude has been to devise algorithms applicable to patterns of a particular type. This paper provides a broader perspective. A general approach to indexing of diffraction patterns of various types is presented. References are made to formally similar problems in other research fields, e.g. in computational geometry, computer science, computer vision or star identification. Besides a general description of available methods, concrete algorithms are presented in detail and their applicability to patterns of various types is demonstrated; a program based on these algorithms is shown to index Kikuchi patterns, Kossel patterns and Laue patterns, among others.

A laboratory transmission diffraction Laue setup to evaluate single-crystal quality

A scanning laboratory Laue transmission setup is developed to probe extended quasi-monocrystalline samples. Orientation mapping is achieved by controlling the collimation of the incident beam and scanning the position of the specimen. An automated indexing algorithm for transmission Laue patterns is presented, together with a forward simulation model adapted for a laboratory setup. The effect of the main parameters of the system is studied with the aim of achieving exposure times of the order of one second. Applications are presented to probe the orientation of an extended part and detect disoriented regions within the bulk. Finally, the analysis of diffraction spot shapes shows that the misorientation within the illuminated volume can be measured, and a new method is proposed to evaluate its complete mean lattice rotation tensor.

Manual measurement of angles in backscattered and transmission Kikuchi diffraction patterns

A historical tool for crystallographic analysis is provided by the Hilton net, which can be used for manually surveying the crystal lattice as it is manifested by the Kikuchi bands in a gnomonic projection. For a quantitative analysis using the Hilton net, the projection centre as the relative position of the signal source with respect to the detector plane needs to be known. Interplanar angles are accessible with a precision and accuracy which is estimated to be ≤0.3°. Angles between any directions, e.g. zone axes, are directly readable. Finally, for the rare case of an unknown projection-centre position, its determination is demonstrated by adapting an old approach developed for photogrammetric applications. It requires the indexing of four zone axes [uvw] _i in a backscattered Kikuchi diffraction pattern of a known phase collected under comparable geometric conditions.

Scanning transmission electron diffraction methods

Scanning diffraction experiments are approaches that take advantage of many of the recent advances in technology (e.g. computer control, detectors, data storage and analysis) for the transmission electron microscope, allowing the crystal structure of materials to be studied with extremely high precision at local positions across large areas of sample. The ability to map the changing crystal structure makes such experiments a powerful tool for the study of microstructure in all its forms from grains and orientations, to secondary phases and interfaces, strain and defects. This review will introduce some of the fundamental concepts behind the breadth of the technique and showcase some of the recent developments in experiment development and applications to materials.

Automated Reconstruction of Spherical Kikuchi Maps

An automated approach to fully reconstruct spherical Kikuchi maps from experimentally collected electron backscatter diffraction patterns and overlay each pattern onto its corresponding position on a simulated Kikuchi sphere is presented in this study. This work demonstrates the feasibility of warping any Kikuchi pattern onto its corresponding location of a simulated Kikuchi sphere and reconstructing a spherical Kikuchi map of a known phase based on any set of experimental patterns. This method consists of the following steps after pattern collection: (1) pattern selection based on multiple threshold values; (2) extraction of multiple scan parameters and phase information; (3) generation of a kinematically simulated Kikuchi sphere as the "skeleton" of the spherical Kikuchi map; and (4) overlaying the inverse gnomonic projection of multiple selected patterns after appropriate pattern center calibration and refinement. The proposed method is the first automated approach to reconstructing spherical Kikuchi maps from experimental Kikuchi patterns. It potentially enables more accurate orientation calculation, new pattern center refinement methods, improved dictionary-based pattern matching, and phase identification in the future.

AstroEBSD: exploring new space in pattern indexing with methods launched from an astronomical approach

Electron backscatter diffraction (EBSD) is a technique used to measure crystallographic features in the scanning electron microscope. The technique is highly automated and readily accessible in many laboratories. EBSD pattern indexing is conventionally performed with raw electron backscatter patterns. These patterns are software processed to locate the band centres (and sometimes edges) from which the crystallographic index of each band is determined. Once a consistent index for many bands is obtained, the crystal orientation with respect to a reference sample and detector orientation can be determined and presented. Unfortunately, because of challenges related to crystal symmetry, there are limited available pattern-indexing approaches and this has probably hampered open development of the technique. In this article, a new method of pattern indexing is presented, based upon a method with which satellites locate themselves in the night sky, and its effectiveness is systematically demonstrated using dynamical simulations and real experimental patterns. The benefit of releasing this new algorithm as open-source software is demonstrated when this indexing process is utilized, together with dynamical solutions, to provide some of the first accuracy assessments of an indexing solution. In disclosing a new indexing algorithm, and software processing toolkit, the authors hope to open up EBSD developments to more users. The software code and example data are released alongside this article for third party developments.

EBSDinterp 1.0: A MATLAB® Program to Perform Microstructurally Constrained Interpolation of EBSD Data

EBSDinterp is a graphic user interface (GUI)-based MATLAB® program to perform microstructurally constrained interpolation of nonindexed electron backscatter diffraction data points. The area available for interpolation is restricted using variations in pattern quality or band contrast (BC). Areas of low BC are not available for interpolation, and therefore cannot be erroneously filled by adjacent grains "growing" into them. Points with the most indexed neighbors are interpolated first and the required number of neighbors is reduced with each successive round until a minimum number of neighbors is reached. Further iterations allow more data points to be filled by reducing the BC threshold. This method ensures that the best quality points (those with high BC and most neighbors) are interpolated first, and that the interpolation is restricted to grain interiors before adjacent grains are grown together to produce a complete microstructure. The algorithm is implemented through a GUI, taking advantage of MATLAB®'s parallel processing toolbox to perform the interpolations rapidly so that a variety of parameters can be tested to ensure that the final microstructures are robust and artifact-free. The software is freely available through the CSIRO Data Access Portal (doi:10.4225/08/5510090C6E620) as both a compiled Windows executable and as source code.

Error analysis of the crystal orientations and disorientations obtained by the classical electron backscatter diffraction technique

The fidelity – that is, the error, precision and accuracy – of the crystallographic orientations and disorientations obtained by the classical two-dimensional Hough-transform-based analysis of electron backscatter diffraction patterns (EBSPs) is studied. Using EBSPs simulated based on the dynamical electron diffraction theory, the fidelity analysis that has been previously performed using the patterns simulated based on the theory of kinematic electron diffraction is improved. Using the same patterns, the efficacy of a Fisher-distribution-based analytical accuracy measure for orientation and disorientation is verified.

Estimation of dislocation density from precession electron diffraction data using the Nye tensor

The Nye tensor offers a means to estimate the geometrically necessary dislocation density of a crystalline sample based on measurements of the orientation changes within individual crystal grains. In this paper, the Nye tensor theory is applied to precession electron diffraction automated crystallographic orientation mapping (PED-ACOM) data acquired using a transmission electron microscope (TEM). The resulting dislocation density values are mapped in order to visualize the dislocation structures present in a quantitative manner. These density maps are compared with other related methods of approximating local strain dependencies in dislocation-based microstructural transitions from orientation data. The effect of acquisition parameters on density measurements is examined. By decreasing the step size and spot size during data acquisition, an increasing fraction of the dislocation content becomes accessible. Finally, the method described herein is applied to the measurement of dislocation emission during in situ annealing of Cu in TEM in order to demonstrate the utility of the technique for characterizing microstructural dynamics.

Determining the Bravais lattice using a single electron backscatter diffraction pattern

Theab initioderivation of the Bravais lattice from the Kikuchi bands detected from a single electron backscatter diffraction (EBSD) pattern is successfully performed. The as-measured band widths and azimuths always suffer from gnomonic distortions which need to be corrected. A primitive reciprocal cell is first reconstructed by means of the corrected data and the cell parameters are then refined by least-squares analysis of hugely over-determined equations. This allows one to further derive a Niggli reduced cell from the primitive cell. The algorithm presented is not related to any crystal symmetry information and is therefore applicable to all crystal systems. The feasibility of the determination of the Bravais lattice type and parameters from a single EBSD pattern is demonstrated using a mineral sample without anya prioriinformation about its crystal structure. The novel application developed in the present work opens the way to the determination of the Bravais lattice of crystalline materials using scanning electron microscopy combined with the EBSD technique.

Dark-field imaging based on post-processed electron backscatter diffraction patterns of bulk crystalline materials in a scanning electron microscope

Dark-field (DF) images were acquired in the scanning electron microscope with an offline procedure based on electron backscatter diffraction (EBSD) patterns (EBSPs). These EBSD-DF images were generated by selecting a particular reflection on the electron backscatter diffraction pattern and by reporting the intensity of one or several pixels around this point at each pixel of the EBSD-DF image. Unlike previous studies, the diffraction information of the sample is the basis of the final image contrast with a pixel scale resolution at the EBSP providing DF imaging in the scanning electron microscope. The offline facility of this technique permits the selection of any diffraction condition available in the diffraction pattern and displaying the corresponding image. The high number of diffraction-based images available allows a better monitoring of deformation structures compared to electron channeling contrast imaging (ECCI) which is generally limited to a few images of the same area. This technique was applied to steel and iron specimens and showed its high capability in describing more rigorously the deformation structures around micro-hardness indents. Due to the offline relation between the reference EBSP and the EBSD-DF images, this new technique will undoubtedly greatly improve our knowledge of deformation mechanism and help to improve our understanding of the ECCI contrast mechanisms.

Electron backscatter diffraction applied to lithium sheets prepared by broad ion beam milling

Due to its very low hardness and atomic number, pure lithium cannot be prepared by conventional methods prior to scanning electron microscopy analysis. Here, we report on the characterization of pure lithium metallic sheets used as base electrodes in the lithium-ion battery technology using electron backscatter diffraction (EBSD) and X-ray microanalysis using energy dispersive spectroscopy (EDS) after the sheet surface was polished by broad argon ion milling (IM). No grinding and polishing were necessary to achieve the sufficiently damage free necessary for surface analysis. Based on EDS results the impurities could be characterized and EBSD revealed the microsctructure and microtexture of this material with accuracy. The beam damage and oxidation/hydration resulting from the intensive use of IM and the transfer of the sample into the microscope chamber was estimated to be <50 nm. Despite the fact that the IM process generates an increase of temperature at the specimen surface, it was assumed that the milling parameters were sufficient to minimize the heating effect on the surface temperature. However, a cryo-stage should be used if available during milling to guaranty a heating artefact free surface after the milling process.

Orientation precision of electron backscatter diffraction measurements near grain boundaries

Electron backscatter diffraction (EBSD) has become a common technique for measuring crystallographic orientations at spatial resolutions on the order of tens of nanometers and at angular resolutions <0.1°. In a recent search of EBSD papers using Google Scholar™, 60% were found to address some aspect of deformation. Generally, deformation manifests itself in EBSD measurements by small local misorientations. An increase in the local misorientation is often observed near grain boundaries in deformed microstructures. This may be indicative of dislocation pile-up at the boundaries but could also be due to a loss of orientation precision in the EBSD measurements. When the electron beam is positioned at or near a grain boundary, the diffraction volume contains the crystal lattices from the two grains separated by the boundary. Thus, the resulting pattern will contain contributions from both lattices. Such mixed patterns can pose some challenge to the EBSD pattern band detection and indexing algorithms. Through analysis of experimental local misorientation data and simulated pattern mixing, this work shows that some of the rise in local misorientation is an artifact due to the mixed patterns at the boundary but that the rise due to physical phenomena is also observed.

Dependence of the electron beam energy and types of surface to determine EBSD indexing reliability in yttria-stabilized zirconia

Electron backscatter diffraction (EBSD) is a powerful technique for surface microstructure analysis. EBSD analysis of cubic yttria-stabilized zirconia (YSZ) is demonstrated. The statistics related to EBSD indexing reliability shows that the probability of accurate grain orientation detection increased significantly when the electron beam energy was increased from 10 to 30 kV. As a result of better sampling with increased interaction volume, a disparity between local and average grain misorientation angle also exhibited the dependence of the electron beam energy to determine the accuracy of grain orientation. To study EBSD indexing reliability as a function of surface roughness and overlayer formation, rapid EBSD measurement tests were performed on (a) YSZ surfaces ion-polished at ion beam energies of 65 nA at 30 kV and 1 nA at 30 kV and (b) carbon-coated versus uncoated YSZ surfaces. The EBSD results at both 10 and 30 kV electron beam energies indicate that EBSD indexing reliability is negatively affected by higher ion beam milling current and amorphous overlayer formation.

Raman spectroscopy as a tool to characterize heterogenite (CoO·OH) (Katanga Province, Democratic Republic of Congo)

Natural heterogenite (CoO·OH) samples were studied by Raman microspectroscopy, electronic microprobe and Electronic BackScattered Diffraction (EBSD). Raw samples and polished sections were made from 10 mines covering the Katanga copperbelt (Katanga Province, Democratic Republic of Congo). Four typical Raman responses have been obtained leading to investigate the laser-induced dehydroxylation of heterogenite into a Co-spinel structure. The results are also compared with EBSD patterns from oven heated heterogenite samples. A close relationship was established between the chemical substitutions of Co by mainly Cu, Ni, Mn and Al and their impact on the mineral Raman response.

Distinguishing crystallographic misorientations of lanthanum zirconate epilayers on nickel substrates by electron backscatter diffraction

Electron backscatter diffraction (EBSD) was used for distinguishing crystallographic orientations and local lattice misfits of a La(2)Zr(2)O(7) (LZO) buffer layer epitaxially grown on a cube textured Ni-5.%W (Ni-W) substrate for a YBCO superconductor film. Orientation data were obtained from the LZO epilayer using low energy primary electrons (5keV) and from the Ni-W substrate by increasing the voltage to 15keV. In-plane and out-of-plane orientations of the LZO epilayer were revealed with respect to its Ni-W substrate. A strong {100} 〈011〉 rotated-cube texture in the LZO epilayer was formed on the {100} 〈001〉 cube-textured Ni-W substrates. LZO and Ni in-plane crystallographic axes are related by an expected 45° rotation. The step-misorientations and the local misfit strains between the LZO epilayer and the substrate were also analyzed.

Epitaxial Growth of GaN on Lattice-Matched Hafnium Substrates

A method of producing epitaxial GaN on single-crystal Hf has been developed. The metal substrate is formed by a strain-anneal process yielding macroscopic (5-mm) grain sizes, followed by polishing, chemical etching, and Ar ion sputtering at elevated temperature in ultrahigh vacuum. The growth is conducted by plasma-assisted molecular beam epitaxy using an initial passivation layer deposited at low temperature and subsequent growth at 700 °C. The resulting films are in registry with the hep substrate lattice as observed by reflection high-energy electron diffraction during growth and verified by plan-view transmission electron microscopy. High-resolution x-ray rocking curve linewidths of the GaN and Hf [1012] peaks are as narrow as 900 and 180 arc seconds, respectively. The [0002] peak separation confirms the approximately 2.7% mismatch in the c axis spacing. Initial photo]uminescence observations at 20 K of a (donor-bound exciton) peak at 3.467 eV are consistent with the assumption of a nearly strain-free film resulting from the exact basal-plane lattice match and close thermal coefficient match between GaN and Hf.

The Role of Texture On The Reliability Of Aluminum Based Interconnects

Preferred crystallographic orientation has long been recognized to play an important role in interconnect reliability where a strong (111) texture improves electromigration lifetime. Detailed microstructural analyses have enabled the role of texture to be better understood. Although Bragg-Brentano scans are often used to characterize texture, it is shown that this technique gives incomplete and sometimes misleading information. The pole figure technique provides a complete description of the texture. The measurement and presentation of textures consider experimental aspects unique to thin film analysis as a prerequisite to developing quality data. Five textural archetypes are identified, and metrics presented for their quantification. Processing effects on texture are complex and depend on all facets of deposition conditions, on substrate/underlayers, and on annealing. General trends and specific examples of the impact of each aspect are given where it will be shown that deposition conditions and the presence of underlayers have the greatest influence. The role of texture on reliability is considered for four failure modes: thermal hillocks, grain collapse, stress voiding, and electromigration. Electromigration results are emphasized where texture must be considered in the context of grain structure, in general, and, more specifically, the ratio of line width to grain size. Most measures of microstructure and reliability are statistical. The importance of local microstructural analysis will be emphasized in terms of both the arrangement of grains relative to the line dimension and microtexture characterization of the grain-to-grain misorientations.

Plastic Deformation and Recrystallization Studied by the 3-D x-ray Microscope

A newly developed synchrotron instrument – the so-called 3D X-ray microscope – is presented. The instrument is placed at the Materials Science beamline at ESRF and dedicated to local μm scale structural characterization within bulk materials. In this paper, emphasis is on in situ studies of thermomechanical processing. The potential of the instrument for characterization of single nuclei and grains is described and discussed based on both first results and planned experiments.

Use of EBSD to study electropulsing induced reverse phase transformations in a Zn-Al alloy (ZA22)

Multi-phase identification and phase transformations in electropulsing treated Zn-Al based alloy wire specimens were studied using electron back-scattered diffraction, back-scattered scanning electron microscopy and X-ray diffraction techniques. By using electron back-scattered diffraction, two phases: η'(S) and η'(T) with a small difference of about 1% in lattice parameters (c(0)/a(0) ) were identified, based on the determined lattice parameters of the phases, and the reverse eutectoid phase transformations: η'(T) +ɛ'(T) +α'(T) →η'(S) and ɛ+α→T'+η were successfully detected. Electron back-scattered diffraction appeared to be an effective technique for studying complex electropulsing induced phase transformations.